A well-known metric for quantifying the similarity between two clusterings of the same data is the adjusted mutual information [1]}, [2]}.
Compared to mutual information, this metric is adjusted against chance, meaning that the similarity cannot be due to randomness but only to the structure of the dataset, appearing in both clusterings. This is the reason why this metric is widely used in unsupervised learning, see [3]}, [4]}, [5]}, [6]}, [7]} for various applications.
